Answer:
The answer would be the first option or the last option: x + 5 or x - 3
Explanation:
Simplify:
x2 - 25
Trying to factor by splitting the middle term
1.1 Factoring x2 - 8x + 15
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 1 • 15 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is -8 .
-15 + -1 = -16
-5 + -3 = -8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -3
x2 - 5x - 3x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
3 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-3) • (x-5)
Which is the desired factorization
Trying to factor as a Difference of Squares:
1.2 Factoring: x2-25
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : x2 is the square of x1
Factorization is : (x + 5) • (x - 5)
Canceling Out :
1.3 Cancel out (x - 5) which appears on both sides of the fraction line.
Final result :
x - 3 / x + 5
HOPE THIS HELPS! HAVE A WONDERFUL DAY!!! :)